A Mathematical Model of Regulatory Mechanisms of Hepatocytes and Hepatitis B

• Main Authors: Mahruy Saidalieva, Mohiniso Baxromovna Hidirova, Abrorjon Makhamatsolievich Turgunov
• Format: Article
• Language: English
• Published: Universitas Indonesia 2019-12-01
• Series: Makara Journal of Science
• Subjects: regulatory mechanisms; mathematical and computer models; qualitative and quantitative analysis; chaos; black hole
• Online Access: https://scholarhub.ui.ac.id/cgi/viewcontent.cgi?article=1151&context=science
• ISSN: 2339-1995; 2356-0851

The study of the functioning of hepatitis B viruses in liver cells using methods of mathematical modeling is considered one of today’s pressing issues. In this article, the domains of functional- differential equations in a mathematical model of regulatory mechanisms of hepatocytes interacting with hepatitis B viruses (HBV) are presented. Characteristic molecular genetic systems regulatory mechanisms of the interrelated activities of liver cells and HBV are analyzed. A series of computational experiments show that the “chaos” and “black hole” theories describe two of the more dangerous regimes. As a result of the analysis of the “chaos” regime, small regions with normal behavior, “r-windows” were revealed. These regions allow the system to move from a “chaos” regime to a “regular” or normal regime. The features of the area of the regulatory activities of molecular genetic mechanisms of hepatocytes and HBV under a chaotic regime were characterized by analyzing the dynamics of the Lyapunov exponent. Small regions with regular behavior, “r-windows” in the field of dynamic chaos were defined. The regulatory nature of hepatocytes and HBV can be moved from the region of dynamic chaos to the normal region by using “r-windows”. The results of a computational experiment quantitatively analyzing the regulatory mechanisms of liver cells and HBV are presented.